Multiple sclerosis is an autoimmune disease that affects white matter in the central nervous system. It is one of the primary causes of neurological disability among young people. Its characteristic pathological lesion is called a plaque, a zone of inflammatory activity and tissue destruction that expands radially outward by destroying the myelin and oligodendrocytes of white matter. The present paper develops a mathematical model of the multiple sclerosis plaques. Although these plaques do not provide reliable information of the clinical disability in MS, they are nevertheless useful as a primary outcome measure of Phase II trials. The model consists of a system of partial differential equations in a simplified geometry of the lesion, consisting of three domains: perivascular space, demyelinated plaque, and white matter. The model describes the activity of various pro- and anti-inflammatory cells and cytokines in the plaque, and quantifies their effect on plaque growth. We show that volume growth of plaques are in qualitative agreement with reported clinical studies of several currently used drugs. We then use the model to explore treatments with combinations of such drugs, and with experimental drugs. We finally consider the benefits of early vs. delayed treatment.

多发性硬化症是一种自身免疫性疾病，会影响中枢神经系统的白质。它是年轻人神经系统残疾的主要原因之一。其特征性病理病变称为斑块，是炎症活动和组织破坏的区域，通过破坏白质的髓磷脂和少突胶质细胞径向向外扩展。本文建立了多发性硬化斑块的数学模型。尽管这些斑块并未提供有关MS临床残疾的可靠信息，但它们仍可作为II期临床试验的主要结局指标。该模型由一个简化的病变几何形状的偏微分方程组组成，由三个区域组成：血管周围空间，脱髓鞘斑块和白质。该模型描述了斑块中各种促炎和抗炎细胞和细胞因子的活性，并量化了它们对斑块生长的影响。我们显示，斑块的体积增长与几种当前使用药物的临床研究报告在质量上吻合。然后，我们使用该模型探索使用此类药物和实验药物的组合的治疗方法。我们最终考虑了早期治疗与延迟治疗的好处。